We consider viscous Hamilton–Jacobi equations of the form [Formula: see text] where a∈ R,
a≠ 0 and p⩾ 1. We provide an extensive investigation of the local Cauchy problem for (VHJ) …

With qa positive real number, the nonlinear partial differential equation in the title of the
paper arises in the study of the growth of surfaces. In that context it is known as the …

The nonlinear partial differential equation in the title is typified mathematically as a viscous
Hamilton–Jacobi equation. It arises in the study of the growth of surfaces, and in that context …

We study qualitative properties of non-negative solutions to the Cauchy problem for the fast
diffusion equation with gradient absorption where N⩾ 1, p∈(1, 2), and q> 0. Based on …

Extinction in finite time and non-compactness of the support are investigated for non-
negative classical solutions to the Cauchy problem ut−∆ u+|∇ u| p= 0 when p∈(0, 1). The …

Global classical solutions to the viscous Hamilton–Jacobi equation ut− Δu= a|∇ u| p in
(0,∞)× Ω with homogeneous Dirichlet boundary conditions are shown to converge to zero in …

The phenomenon of finite time extinction of bounded and non-negative solutions to the
diffusion equation with strong absorption\partial_t u-Δ u^ m+| x|^ σ u^ q= 0,\qquad (t, x) ∈ (0 …

The large time behavior of non-negative solutions to the viscous Hamilton-Jacobi
equation∂ tu–Δu+|▽ u| q= 0 in (0,∞)× ℝN is investigated for the critical exponent q=(N+ …

Solutions in self-similar form presenting finite time extinction to the singular diffusion
equation with gradient absorption $$\partial_t u-\mathrm {div}(|\nabla u|^{p-2}\nabla …

Eternal solutions to a singular diffusion equation with critical gradient absorption Page 1
Nonlinearity PAPER Eternal solutions to a singular diffusion equation with critical gradient …